1. Field of the Invention
The invention relates generally to the field of well logging apparatus and methods, and in particular, to processing of nuclear magnetic resonance (NMR) signals to estimate physical properties of an oil or gas reservoir.
2. Description of the Related Art
Estimating physical parameters such as effective and total porosity, pore-size distribution, and the determining hydrocarbon types, are principal purposes for NMR log interpretation. The underlying rationale that NMR logging may provide such information is based on evidence that NMR relaxation times in porous media depend on texture (e.g., pore and grain-size distributions, in single wetting fluid phase saturated systems) and additionally on fluid types (oil/water/gas) in multiphase fluid-saturated porous media. Observed NMR log data (e.g., Carr, Purcell, Meiboom and Gill [CPMG] echo trains) represent the contributions from multiple fluid phases as well as fluids in different sized pores and thus, typically, exhibit a multiexponential behavior, with transverse relaxation times, T.sub.2 components spanning from approximately one millisecond (ms) to over one second. The practical challenge for NMR log interpretation is to discriminate between contributions due to texture and fluid saturations and to quantify fluid saturations. Moreover, the NMR log signal typically is weak, and the instrumentation systems and the logging environment contribute significant noise that may be comparable to the signal. The resulting poor signal-to-noise ratio (S/N) gives rise to significant uncertainty in the estimated petrophysical parameters.
Prior art methods of NMR log interpretation generally use an inversion technique to estimate a relaxation distribution, i.e., a T.sub.2 spectrum, from the acquired CPMG echo train data fit to a multiexponential decay relaxation distribution model. Different fluid phases may have different relaxation times, depending on the fluid molecular interaction, the rock surface properties, the reservoir environment, the fluid wetting characteristics of the formation and other physical properties known in the art. Distinctive features on the T.sub.2 spectra, often reveal fluid saturations and pore structures--information on which petrophysical interpretation is based. For example, in the case of a water-wet reservoir with multiphase saturation, the non-wetting, and light, oil signal distributes into long relaxation bins. Water, on the other hand, in a water-wet reservoir, interacts strongly with pore surfaces, and thus has a short relaxation time. On a T.sub.2 spectrum, water is identified from the short T.sub.2 region, that is, initial bins. Gas, which is also non-wetting but diffuses faster than oil and water, may be identified in the intermediate region on a T.sub.2 spectrum, since faster diffusion of gas reduces the apparent T.sub.2 relaxation. From the estimated T.sub.2 spectrum, partial porosities associated with different parts of the T.sub.2 spectrum are identified for estimating the fluid saturations in a multiphase zone. In a single wetting fluid phase zone, for example, a water zone, with relative homogenous rock mineralogy, a T.sub.2 spectrum approximately represents the porosity distribution in terms of pore sizes. Therefore, reliable interpretation depends heavily on accurate T.sub.2 spectrum estimation.
It is well known that inverting echo train data to the T.sub.2 domain distribution is an ill-conditioned problem, particularly when noise is present. Although regularization methods may help to stabilize the solutions, they also smooth the T.sub.2 distribution estimate considerably, causing most of the distinguishing features of the T.sub.2 distribution to be lost. The possible distortion of the resulting T.sub.2 distribution estimate makes it difficult to separate the saturating fluid types. Furthermore, when a distribution involves short and long T.sub.2 components, the standard procedure of using the method of minimization of least squares residuals in the inversion process often fails to weight all of the T.sub.2 components equally. The short T.sub.2 components are effectively represented by fewer echoes than the long T.sub.2 components. When a T.sub.2 distribution is dominated by a very short T.sub.2 component and a second, long T.sub.2 component, the technique can fail to fit the short component faithfully.
FIG. 1A shows data from a synthesized noisy echo train fitted to a multiexponential model using a singular value decomposition (SVD) inversion algorithm, as is common in prior art methods. For an example of an application of SVD to NMR echo trains, see U.S. Pat. No. 5,517,115 issued to Prammer. The solid circles in FIG. 1 are the samples of the noisy echo train at the echo interval of 1.2 milliseconds (ms). The noisy signal is generated from a multiexponential model NMR signal in accordance with Equation (1) below, and added zero-mean Gaussian noise, as in Equation (2) below. The standard deviation of the noise is 1.2.
The solid curves plot the underlying time-dependent noise-free multiexponential signal (thin line), and the fit to the noisy signal obtained using the SVD inversion method of the prior art (bold line). When the standard deviation of the random noise is high, the estimate noticeably misrepresents the actual spectrum. The short components of the input data, t 10 ms, suffer most, underestimating the effective porosity. This is also seen in the T.sub.2 spectrum.
FIG. 1B shows an underlying bimodal distribution (dual peak) (.smallcircle.) and the estimated T.sub.2 spectrum (.times.). The underlying distribution is bimodal with peaks near a T.sub.2 of 3 ms and 150 ms. The multiexponential model includes seventeen terms, of which five have zero amplitude. The resulting fit to the spectrum from the SVD inversion has a single, broad, peak near T.sub.2 equal to 100 msec. The T.sub.2 spectrum below approximately 11 ms significantly underestimates the actual spectrum, and in the range of approximately 20-90 ms overestimates the actual spectrum.
Thus, there is a need in the art for improved methods of NMR signal processing for the recovery of T.sub.2 spectra and thereby subterranean petrophysical characteristics in a oil or gas reservoir.